# quark momentum and quark mass in unpairing and pairing phase

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In this Review paper in p.1464, top left: Rev.Mod.Phys.80:1455-1515,2008 -- Color superconductivity in dense quark matter

It shows a figure of quark momentum of quark $u,d,s$, in unpairing and pairing phase, such that

$$p_d >p_u>p_s$$

however, we know: $$m_u<m_d<m_s$$

so why isnt that $$p_u >p_d>p_s$$ if momentum is inverse proportional to the quark mass? What is going on here for these quark momentum?

This post imported from StackExchange Physics at 2020-11-05 13:26 (UTC), posted by SE-user annie marie heart
asked Dec 25, 2017

We usually consider electrically neutral matter (because charged matter cannot exist in a macroscopic system -- the Coulomb energy diverges with the volume). In principle $uds$ matter with a deficit of strange quarks (because of the heavier strange quark) can be neutralized by electrons, but it is energetically favorable to neutralize by an excess of $d$ quarks (also negatively charged). The reason is that reference state, neutral matter with equal Fermi momenta for $u,d,s$ quarks, has a large Fermi momentum for down quarks, but zero Fermi momentum for electrons. A small shift in the chemical potentials then leads to a large shift of the down quark abundance, but only a small shift in the electron abundance.
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